In The Guardian piece, Johansson implored people not to rush judgment about matters that haven't been stress tested in court.
"It's not like this is somebody that's been prosecuted and found guilty of something, and you can then go, 'I don't support this lifestyle or whatever.' I mean, it's all guesswork," she said. "I don't know anything about it. It would be ridiculous for me to make any kind of assumption one way or the other.
"I think it's irresponsible to take a bunch of actors that will have a Google alert on and to suddenly throw their name into a situation that none of us could possibly knowingly comment on. That just feels irresponsible to me."
Farrow's brother Ronan wrote an expose for the New Yorker on the allegations against film mogul Harvey Weinstein and has supported his sister, reports Fox News.
Johansson appeared in three Allen films,Match Point, Scoop and Vicky Cristina Barcelona.
Among those pointing out the "hypocrisy" of the speech was TV presenter Piers Morgan.
"Scarlett Johansson is so repulsed by James Franco she wants her #TimesUp pin back," he wrote on Twitter.
"She wasn't quite so repulsed by child rapist Roman Polanski or Woody Allen, who married his wife's adoptive daughter & whose own adoptive daughter says he abused her at 7.
"I don't understand how Scarlett Johansson can condemn James Franco yet, in the past, sand (sic) up for Woody Allen. What a hypocrite," wrote another commentator on Twitter.
"Yes, this is the same Scarlett Johansson who starred in three Woody Allen films and said of the accusations against him: 'It's all guesswork,' wrote another.
Franco has been criticised for wearing a Time's Up pin to the Golden Globes, where he won Best Actor in a Comedy or Musical for The Disaster Artist.
"How could a person publicly stand by an organisation that helps to provide support for victims of sexual assault while privately preying on people who have no power?" Johansson told a crowd in Los Angeles.
While she didn't refer to Franco by name her representative later confirmed to the Los Angeles Times that she was speaking about the actor.
"I want my pin back, by the way," she said.
In the speech, Johansson also described her "rage" at her own experiences as a young woman in Hollywood, after landing her first role at age 12.
"And suddenly I was 19 again, and I started to remember all the men I'd known who'd taken advantage of the fact that I was a young woman who didn't yet have the tools to say no, or to understand the value of my own self worth," she said.
"I'd had many relationships both personal and professional where the power dynamic was so off that I had to create a narrative that I was the cool girl who could hang in and hang out, and that sometimes meant compromising what felt right for me."
Johansson finished the speech by championing the #MeToo movement.
"It gives me hope that we are moving towards a place where our sense of equality can truly come from within ourselves," she said.
